Computer Aided Assessment of Mathematics

Chris Sangwin

Abstract

This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to automatically establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded. This is not so simple. Even articulating precisely the desired criteria forces the teacher to think very carefully indeed. Hence, CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. For example, the constraints of the paper-based for ... More

This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to automatically establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded. This is not so simple. Even articulating precisely the desired criteria forces the teacher to think very carefully indeed. Hence, CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. For example, the constraints of the paper-based formats have affected what we do and why. It is natural for busy teachers to set only those questions which can be marked by hand in a straightforward way. However, there are other kinds of questions, e.g., those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking by hand. And yet such questions have their place and value in provoking thought and learning. Furthermore, we explain how, in certain cases, these can be automatically assessed. Case studies of existing systems will illustrate this in a concrete and practical way.

End Matter

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